The radius of a circle is 9cm. Find the length of an arc of this circle which cuts off a chord of length, equal to length of radius.
Answers
Formula to find arc length:
Arc length = 2πr (θ / 360°),
where r is the radius of the circle and θ is the central angle in degree.
Drawing a figure:
Before we solve the problem, we draw a circle with centre A. We draw two radius in such a way that their circumferential ends can be joined in same distance as of radius's length. We draw two end points B, C. Joining A, B, C, we get a triangle ABC which is an equilateral triangle, making an angle ∠BAC = 60° at the centre and BC is the chord mentioned in the question.
Solution:
We have to find the arc length of BC.
Here radius of the circle, r = 9 cm,
central angle, θ = 60°
Hence, arc length of BC is
= 2πr (θ/360°)
= 2π (9) * (60° / 360°) cm
= 2 * (22/7) * 9 * (1/6) cm
= 9.43 cm
